<h2>Problem 147</h2>
<div style="color:#666;font-size:80%;">31 March 2007</div><br />
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<p>In a 3x2 cross-hatched grid, a total of 37 different rectangles could be situated within that grid as indicated in the sketch.</p>
<div style="text-align:center;"><img src="project/images/p_147.gif" width="361" height="176" alt="" /></div>
<p>There are 5 grids smaller than 3x2, vertical and horizontal dimensions being important, i.e. 1x1, 2x1, 3x1, 1x2 and 2x2. If each of them is cross-hatched, the following number of different rectangles could be situated within those smaller grids:</p>
<p>1x1: 1
<br />2x1: 4
<br />3x1: 8
<br />1x2: 4
<br />2x2: 18</p>

<p>Adding those to the 37 of the 3x2 grid, a total of 72 different rectangles could be situated within 3x2 and smaller grids.</p>

<p>How many different rectangles could be situated within 47x43 and smaller grids?</p>
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